New fixed point theorem under R-contractions

In this manuscript we introduce the notions of R-function and R-contractions, and we show an ad hoc fixed point theorem. We prove that this new kind of contractions properly includes the family of all Meir-Keeler contractions and other well-known classes of contractions that have been given very recently (for instance, those using simulation functions and manageable functions). As a consequence, our approach turns out to be appropriate to unify the treatment of different kinds of contractive nonlinear operators.This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. The second author, therefore, acknowledges with thanks DSR for technical and financial support. The authors are grateful to three anonymous referees for their useful suggestions and comments. AF Roldán López de Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada. The same author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE

Contrasting effects of long term versus short-term nitrogen addition on photosynthesis and respiration in the Arctic

We examined the effects of short (<1–4 years) and long-term (22 years) nitrogen (N) and/or phosphorus (P) addition on the foliar CO2 exchange parameters of the Arctic species Betula nana and Eriophorum vaginatum in northern Alaska. Measured variables included: the carboxylation efficiency of Rubisco (Vcmax), electron transport capacity (Jmax), dark respiration (Rd), chlorophyll a and b content (Chl), and total foliar N (N). For both B. nana and E. vaginatum, foliar N increased by 20–50 % as a consequence of 1–22 years of fertilisation, respectively, and for B. nana foliar N increase was consistent throughout the whole canopy. However, despite this large increase in foliar N, no significant changes in Vcmax and Jmax were observed. In contrast, Rd was significantly higher (>25 %) in both species after 22 years of N addition, but not in the shorter-term treatments. Surprisingly, Chl only increased in both species the first year of fertilisation (i.e. the first season of nutrients applied), but not in the longer-term treatments. These results imply that: (1) under current (low) N availability, these Arctic species either already optimize their photosynthetic capacity per leaf area, or are limited by other nutrients; (2) observed increases in Arctic NEE and GPP with increased nutrient availability are caused by structural changes like increased leaf area index, rather than increased foliar photosynthetic capacity and (3) short-term effects (1–4 years) of nutrient addition cannot always be extrapolated to a larger time scale, which emphasizes the importance of long-term ecological experiments

Fixed point theorems for cyclic self-maps involving weaker Meir-Keelerfunctions in complete metric spaces and applications

We obtain fixed point theorems for cyclic self-maps on complete metric spaces involving Meir-Keeler and weaker Meir-Keeler functions, respectively. In this way, we extend several well-known fixed point theorems and, in particular, improve some very recent results on weaker Meir-Keeler functions. Fixed point results for well-posed property and for limit shadowing property are also deduced. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.The second author thanks for the support of the Ministry of Economy and Competitiveness of Spain under grant MTM2012-37894-C02-01, and the Universitat Politecnica de Valencia, grant PAID-06-12-SP20120471.Nashine, HK.; Romaguera Bonilla, S. (2013). Fixed point theorems for cyclic self-maps involving weaker Meir-Keelerfunctions in complete metric spaces and applications. Fixed Point Theory and Applications. 2013(224):1-15. https://doi.org/10.1186/1687-1812-2013-224S1152013224Kirk WA, Srinavasan PS, Veeramani P: Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory 2003, 4: 79–89.Banach S: Sur les operations dans les ensembles abstraits et leur application aux equations integerales. Fundam. Math. 1922, 3: 133–181.Boyd DW, Wong SW: On nonlinear contractions. Proc. Am. Math. Soc. 1969, 20: 458–464. 10.1090/S0002-9939-1969-0239559-9Caristi J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 1976, 215: 241–251.Di Bari C, Suzuki T, Vetro C: Best proximity points for cyclic Meir-Keeler contractions. Nonlinear Anal. 2008, 69: 3790–3794. 10.1016/j.na.2007.10.014Karapinar E: Fixed point theory for cyclic weaker ϕ -contraction. Appl. Math. Lett. 2011, 24: 822–825. 10.1016/j.aml.2010.12.016Karapinar E, Sadarangani K: Corrigendum to “Fixed point theory for cyclic weaker ϕ -contraction” [Appl. Math. Lett. Vol. 24(6), 822–825.]. Appl. Math. Lett. 2012, 25: 1582–1584. 10.1016/j.aml.2011.11.001Karapinar E, Sadarangani K:Fixed point theory for cyclic ( ϕ − φ ) -contractions. Fixed Point Theory Appl. 2011., 2011: Article ID 69Nahsine HK: Cyclic generalized ψ -weakly contractive mappings and fixed point results with applications to integral equations. Nonlinear Anal. 2012, 75: 6160–6169. 10.1016/j.na.2012.06.021Păcurar M: Fixed point theory for cyclic Berinde operators. Fixed Point Theory 2011, 12: 419–428.Păcurar M, Rus IA: Fixed point theory for cyclic φ -contractions. Nonlinear Anal. 2010, 72: 2683–2693.Piatek B: On cyclic Meir-Keeler contractions in metric spaces. Nonlinear Anal. 2011, 74: 35–40. 10.1016/j.na.2010.08.010Rus IA: Cyclic representations and fixed points. Ann. “Tiberiu Popoviciu” Sem. Funct. Equ. Approx. Convexity 2005, 3: 171–178.Chen CM: Fixed point theory for the cyclic weaker Meir-Keeler function in complete metric spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 17Chen CM: Fixed point theorems for cyclic Meir-Keeler type mappings in complete metric spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 41Meir A, Keeler E: A theorem on contraction mappings. J. Math. Anal. Appl. 1969, 28: 326–329. 10.1016/0022-247X(69)90031-6Matkowski J: Integrable solutions of functional equations. Diss. Math. 1975, 127: 1–68.Karapinar E, Romaguera S, Tas K: Fixed points for cyclic orbital generalized contractions on complete metric spaces. Cent. Eur. J. Math. 2013, 11: 552–560. 10.2478/s11533-012-0145-0De Blasi FS, Myjak J: Sur la porosité des contractions sans point fixed. C. R. Math. Acad. Sci. Paris 1989, 308: 51–54.Lahiri BK, Das P: Well-posedness and porosity of certain classes of operators. Demonstr. Math. 2005, 38: 170–176.Popa V: Well-posedness of fixed point problems in orbitally complete metric spaces. Stud. Cercet. ştiinţ. - Univ. Bacău, Ser. Mat. 2006, 16: 209–214. Supplement. Proceedings of ICMI 45, Bacau, Sept. 18–20 (2006)Popa VV: Well-posedness of fixed point problems in compact metric spaces. Bul. Univ. Petrol-Gaze, Ploiesti, Sec. Mat. Inform. Fiz. 2008, 60: 1–4

Quality of dietary fat and genetic risk of type 2 diabetes: individual participant data meta-analysis.

OBJECTIVE: To investigate whether the genetic burden of type 2 diabetes modifies the association between the quality of dietary fat and the incidence of type 2 diabetes. DESIGN: Individual participant data meta-analysis. DATA SOURCES: Eligible prospective cohort studies were systematically sourced from studies published between January 1970 and February 2017 through electronic searches in major medical databases (Medline, Embase, and Scopus) and discussion with investigators. REVIEW METHODS: Data from cohort studies or multicohort consortia with available genome-wide genetic data and information about the quality of dietary fat and the incidence of type 2 diabetes in participants of European descent was sought. Prospective cohorts that had accrued five or more years of follow-up were included. The type 2 diabetes genetic risk profile was characterized by a 68-variant polygenic risk score weighted by published effect sizes. Diet was recorded by using validated cohort-specific dietary assessment tools. Outcome measures were summary adjusted hazard ratios of incident type 2 diabetes for polygenic risk score, isocaloric replacement of carbohydrate (refined starch and sugars) with types of fat, and the interaction of types of fat with polygenic risk score. RESULTS: Of 102 305 participants from 15 prospective cohort studies, 20 015 type 2 diabetes cases were documented after a median follow-up of 12 years (interquartile range 9.4-14.2). The hazard ratio of type 2 diabetes per increment of 10 risk alleles in the polygenic risk score was 1.64 (95% confidence interval 1.54 to 1.75, I2=7.1%, τ2=0.003). The increase of polyunsaturated fat and total omega 6 polyunsaturated fat intake in place of carbohydrate was associated with a lower risk of type 2 diabetes, with hazard ratios of 0.90 (0.82 to 0.98, I2=18.0%, τ2=0.006; per 5% of energy) and 0.99 (0.97 to 1.00, I2=58.8%, τ2=0.001; per increment of 1 g/d), respectively. Increasing monounsaturated fat in place of carbohydrate was associated with a higher risk of type 2 diabetes (hazard ratio 1.10, 95% confidence interval 1.01 to 1.19, I2=25.9%, τ2=0.006; per 5% of energy). Evidence of small study effects was detected for the overall association of polyunsaturated fat with the risk of type 2 diabetes, but not for the omega 6 polyunsaturated fat and monounsaturated fat associations. Significant interactions between dietary fat and polygenic risk score on the risk of type 2 diabetes (P>0.05 for interaction) were not observed. CONCLUSIONS: These data indicate that genetic burden and the quality of dietary fat are each associated with the incidence of type 2 diabetes. The findings do not support tailoring recommendations on the quality of dietary fat to individual type 2 diabetes genetic risk profiles for the primary prevention of type 2 diabetes, and suggest that dietary fat is associated with the risk of type 2 diabetes across the spectrum of type 2 diabetes genetic risk.The EPIC-InterAct study received funding from the European Union (Integrated Project LSHM-CT-2006-037197 in the Framework Programme 6 of the European Community). We thank all EPIC participants and staff for their contribution to the study. We thank Nicola Kerrison (MRC Epidemiology Unit, University of Cambridge, Cambridge, UK) for managing the data for the InterAct Project. In addition, InterAct investigators acknowledge funding from the following agencies: MT: Health Research Fund (FIS) of the Spanish Ministry of Health; the CIBER en Epidemiología y Salud Pública (CIBERESP), Spain; Murcia Regional Government (N° 6236); JS: JS was supported by a Heisenberg-Professorship (SP716/2-1), a Clinical Research Group (KFO218/1) and a research group (Molecular Nutrition to JS) of the Bundesministerium für Bildung und Forschung (BMBF); YTvdS, JWJB, PHP, IS: Verification of diabetes cases was additionally funded by NL Agency grant IGE05012 and an Incentive Grant from the Board of the UMC Utrecht; HBBdM: Dutch Ministry of Public Health, Welfare and Sports (VWS), Netherlands Cancer Registry (NKR), LK Research Funds, Dutch Prevention Funds, Dutch ZON (Zorg Onderzoek Nederland), World Cancer Research Fund (WCRF), Statistics Netherlands (The Netherlands); MDCL: Health Research Fund (FIS) of the Spanish Ministry of Health; Murcia Regional Government (N° 6236); FLC: Cancer Research UK; PD: Wellcome Trust; LG: Swedish Research Council; GH: The county of Västerbotten; RK: Deutsche Krebshilfe; TJK: Cancer Research UK; KK: Medical Research Council UK, Cancer Research UK; AK: Medical Research Council (Cambridge Lipidomics Biomarker Research Initiative); CN: Health Research Fund (FIS) of the Spanish Ministry of Health; Murcia Regional Government (N° 6236); KO: Danish Cancer Society; OP: Faculty of Health Science, 47 University of Aarhus, Denmark; JRQ: Asturias Regional Government; LRS: Asturias Regional Government; AT: Danish Cancer Society; RT: AIRE-ONLUS Ragusa, AVIS-Ragusa, Sicilian Regional Government; DLvdA, WMMV: Dutch Ministry of Public Health, Welfare and Sports (VWS), Netherlands Cancer Registry (NKR), LK Research Funds, Dutch Prevention Funds, Dutch ZON (Zorg Onderzoek Nederland), World Cancer Research Fund (WCRF), Statistics Netherlands (The Netherlands); MMC: Wellcome Trust (083270/Z/07/Z), MRC (G0601261)

Convergence in phosphorus constraints to photosynthesis in forests around the world

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: The photosynthesis and leaf nutrient data reported in the paper are available at https://doi.org/10.6084/m9.figshare.20010485.v1, and the model results are available on the European open-access repository Zenodo at https://doi.org/10.5281/zenodo.6619615. All other data reported in the paper are presented in the supplementary materials.Code availability: The R code used for analyses is at https://github.com/ellswor2/photo_p_repo2.git. The source code for ORCHIDEE is at https://doi.org/10.14768/20200407002.1.Tropical forests take up more carbon (C) from the atmosphere per annum by photosynthesis than any other type of vegetation. Phosphorus (P) limitations to C uptake are paramount for tropical and subtropical forests around the globe. Yet the generality of photosynthesis-P relationships underlying these limitations are in question, and hence are not represented well in terrestrial biosphere models. Here we demonstrate the dependence of photosynthesis and underlying processes on both leaf N and P concentrations. The regulation of photosynthetic capacity by P was similar across four continents. Implementing P constraints in the ORCHIDEE-CNP model, gross photosynthesis was reduced by 36% across the tropics and subtropics relative to traditional N constraints and unlimiting leaf P. Our results provide a quantitative relationship for the P dependence for photosynthesis for the front-end of global terrestrial C models that is consistent with canopy leaf measurements